What is the general solution for cos(3x)sin(2x)=0 ?

The general solution for cos(3x)sin(2x)=0 is x= pi/6+(2pin)/3 ,x= pi/2+(2pin)/3 ,x=pin,x= pi/2+pin

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cos(3x)sin(2x)=0

cos (3 x) sin (2 x) = 0

x = \frac{π}{6} + \frac{2 πn}{3}, x = \frac{π}{2} + \frac{2 πn}{3}, x = πn, x = \frac{π}{2} + πn

Solution steps

cos (3 x) sin (2 x) = 0

Solving each part separately

cos (3 x) = 0 or sin (2 x) = 0

cos (3 x) = 0 : x = \frac{π}{6} + \frac{2 πn}{3}, x = \frac{π}{2} + \frac{2 πn}{3}

sin (2 x) = 0 : x = πn, x = \frac{π}{2} + πn

Combine all the solutions

x = \frac{π}{6} + \frac{2 πn}{3}, x = \frac{π}{2} + \frac{2 πn}{3}, x = πn, x = \frac{π}{2} + πn

2 sin (2 θ) = 2

sin^{2} (θ) + sin (θ) - 2 = 0

sin^{2} (θ) - tan (θ) cos^{2} (θ) = 0

3 tan (x) = 4 sin (x)

2 sin (3 θ) + 1 = 0

What is the general solution for cos(3x)sin(2x)=0 ?
The general solution for cos(3x)sin(2x)=0 is x= pi/6+(2pin)/3 ,x= pi/2+(2pin)/3 ,x=pin,x= pi/2+pin